Step |
Hyp |
Ref |
Expression |
1 |
|
xrge0tsms.g |
|
2 |
|
xrge0tsms.a |
|
3 |
|
xrge0tsms.f |
|
4 |
|
xrge0tsms.s |
|
5 |
|
iccssxr |
|
6 |
|
xrsbas |
|
7 |
1 6
|
ressbas2 |
|
8 |
5 7
|
ax-mp |
|
9 |
|
eqid |
|
10 |
9
|
xrge0subm |
|
11 |
|
xrex |
|
12 |
11
|
difexi |
|
13 |
|
simpl |
|
14 |
|
ge0nemnf |
|
15 |
13 14
|
jca |
|
16 |
|
elxrge0 |
|
17 |
|
eldifsn |
|
18 |
15 16 17
|
3imtr4i |
|
19 |
18
|
ssriv |
|
20 |
|
ressabs |
|
21 |
12 19 20
|
mp2an |
|
22 |
1 21
|
eqtr4i |
|
23 |
9
|
xrs10 |
|
24 |
22 23
|
subm0 |
|
25 |
10 24
|
ax-mp |
|
26 |
|
xrge0cmn |
|
27 |
1 26
|
eqeltri |
|
28 |
27
|
a1i |
|
29 |
|
elinel2 |
|
30 |
29
|
adantl |
|
31 |
|
elfpw |
|
32 |
31
|
simplbi |
|
33 |
|
fssres |
|
34 |
3 32 33
|
syl2an |
|
35 |
|
c0ex |
|
36 |
35
|
a1i |
|
37 |
34 30 36
|
fdmfifsupp |
|
38 |
8 25 28 30 34 37
|
gsumcl |
|
39 |
5 38
|
sselid |
|
40 |
39
|
fmpttd |
|
41 |
40
|
frnd |
|
42 |
|
supxrcl |
|
43 |
41 42
|
syl |
|
44 |
4 43
|
eqeltrid |
|
45 |
|
0ss |
|
46 |
|
0fin |
|
47 |
|
elfpw |
|
48 |
45 46 47
|
mpbir2an |
|
49 |
|
0cn |
|
50 |
|
eqid |
|
51 |
|
reseq2 |
|
52 |
|
res0 |
|
53 |
51 52
|
eqtrdi |
|
54 |
53
|
oveq2d |
|
55 |
25
|
gsum0 |
|
56 |
54 55
|
eqtrdi |
|
57 |
50 56
|
elrnmpt1s |
|
58 |
48 49 57
|
mp2an |
|
59 |
|
supxrub |
|
60 |
41 58 59
|
sylancl |
|
61 |
60 4
|
breqtrrdi |
|
62 |
|
elxrge0 |
|
63 |
44 61 62
|
sylanbrc |
|
64 |
|
letop |
|
65 |
|
ovex |
|
66 |
|
elrest |
|
67 |
64 65 66
|
mp2an |
|
68 |
|
elinel1 |
|
69 |
|
reex |
|
70 |
|
simplrl |
|
71 |
|
elrestr |
|
72 |
64 69 70 71
|
mp3an12i |
|
73 |
|
eqid |
|
74 |
73
|
xrtgioo |
|
75 |
72 74
|
eleqtrrdi |
|
76 |
|
simplrr |
|
77 |
|
simpr |
|
78 |
76 77
|
elind |
|
79 |
|
tg2 |
|
80 |
75 78 79
|
syl2anc |
|
81 |
|
ioof |
|
82 |
|
ffn |
|
83 |
|
ovelrn |
|
84 |
81 82 83
|
mp2b |
|
85 |
|
simprrr |
|
86 |
85
|
adantr |
|
87 |
|
inss1 |
|
88 |
86 87
|
sstrdi |
|
89 |
27
|
a1i |
|
90 |
|
simprrl |
|
91 |
|
elinel2 |
|
92 |
90 91
|
syl |
|
93 |
|
simp-4l |
|
94 |
93 3
|
syl |
|
95 |
|
elfpw |
|
96 |
95
|
simplbi |
|
97 |
90 96
|
syl |
|
98 |
94 97
|
fssresd |
|
99 |
35
|
a1i |
|
100 |
98 92 99
|
fdmfifsupp |
|
101 |
8 25 89 92 98 100
|
gsumcl |
|
102 |
5 101
|
sselid |
|
103 |
|
simprll |
|
104 |
103
|
adantr |
|
105 |
|
simprrr |
|
106 |
92 105
|
ssfid |
|
107 |
105 97
|
sstrd |
|
108 |
94 107
|
fssresd |
|
109 |
108 106 99
|
fdmfifsupp |
|
110 |
8 25 89 106 108 109
|
gsumcl |
|
111 |
5 110
|
sselid |
|
112 |
|
simprlr |
|
113 |
93 2
|
syl |
|
114 |
1 113 94 90 105
|
xrge0gsumle |
|
115 |
104 111 102 112 114
|
xrltletrd |
|
116 |
93 44
|
syl |
|
117 |
|
simprlr |
|
118 |
117
|
adantr |
|
119 |
93 41
|
syl |
|
120 |
|
ovex |
|
121 |
|
reseq2 |
|
122 |
121
|
oveq2d |
|
123 |
50 122
|
elrnmpt1s |
|
124 |
90 120 123
|
sylancl |
|
125 |
|
supxrub |
|
126 |
119 124 125
|
syl2anc |
|
127 |
126 4
|
breqtrrdi |
|
128 |
|
simprrl |
|
129 |
|
eliooord |
|
130 |
128 129
|
syl |
|
131 |
130
|
simprd |
|
132 |
131
|
adantr |
|
133 |
102 116 118 127 132
|
xrlelttrd |
|
134 |
|
elioo1 |
|
135 |
104 118 134
|
syl2anc |
|
136 |
102 115 133 135
|
mpbir3and |
|
137 |
88 136
|
sseldd |
|
138 |
137 101
|
elind |
|
139 |
138
|
anassrs |
|
140 |
139
|
expr |
|
141 |
140
|
ralrimiva |
|
142 |
130
|
simpld |
|
143 |
142 4
|
breqtrdi |
|
144 |
41
|
ad3antrrr |
|
145 |
|
supxrlub |
|
146 |
144 103 145
|
syl2anc |
|
147 |
143 146
|
mpbid |
|
148 |
|
ovex |
|
149 |
148
|
rgenw |
|
150 |
|
reseq2 |
|
151 |
150
|
oveq2d |
|
152 |
151
|
cbvmptv |
|
153 |
|
breq2 |
|
154 |
152 153
|
rexrnmptw |
|
155 |
149 154
|
ax-mp |
|
156 |
147 155
|
sylib |
|
157 |
141 156
|
reximddv |
|
158 |
157
|
expr |
|
159 |
|
eleq2 |
|
160 |
|
sseq1 |
|
161 |
159 160
|
anbi12d |
|
162 |
161
|
imbi1d |
|
163 |
158 162
|
syl5ibrcom |
|
164 |
163
|
rexlimdvva |
|
165 |
84 164
|
syl5bi |
|
166 |
165
|
rexlimdv |
|
167 |
80 166
|
mpd |
|
168 |
|
simplrl |
|
169 |
|
simpr |
|
170 |
|
simplrr |
|
171 |
169 170
|
eqeltrrd |
|
172 |
|
pnfnei |
|
173 |
168 171 172
|
syl2anc |
|
174 |
|
simprr |
|
175 |
174
|
ad2antrr |
|
176 |
27
|
a1i |
|
177 |
91
|
ad2antrl |
|
178 |
|
simp-5l |
|
179 |
178 3
|
syl |
|
180 |
96
|
ad2antrl |
|
181 |
179 180
|
fssresd |
|
182 |
35
|
a1i |
|
183 |
181 177 182
|
fdmfifsupp |
|
184 |
8 25 176 177 181 183
|
gsumcl |
|
185 |
5 184
|
sselid |
|
186 |
|
rexr |
|
187 |
186
|
ad2antrl |
|
188 |
187
|
ad2antrr |
|
189 |
|
simprr |
|
190 |
177 189
|
ssfid |
|
191 |
189 180
|
sstrd |
|
192 |
179 191
|
fssresd |
|
193 |
192 190 182
|
fdmfifsupp |
|
194 |
8 25 176 190 192 193
|
gsumcl |
|
195 |
5 194
|
sselid |
|
196 |
|
simplrr |
|
197 |
178 2
|
syl |
|
198 |
|
simprl |
|
199 |
1 197 179 198 189
|
xrge0gsumle |
|
200 |
188 195 185 196 199
|
xrltletrd |
|
201 |
|
pnfge |
|
202 |
185 201
|
syl |
|
203 |
|
pnfxr |
|
204 |
|
elioc1 |
|
205 |
188 203 204
|
sylancl |
|
206 |
185 200 202 205
|
mpbir3and |
|
207 |
175 206
|
sseldd |
|
208 |
207 184
|
elind |
|
209 |
208
|
expr |
|
210 |
209
|
ralrimiva |
|
211 |
|
ltpnf |
|
212 |
211
|
ad2antrl |
|
213 |
|
simplr |
|
214 |
212 213
|
breqtrrd |
|
215 |
214 4
|
breqtrdi |
|
216 |
41
|
ad3antrrr |
|
217 |
216 187 145
|
syl2anc |
|
218 |
215 217
|
mpbid |
|
219 |
218 155
|
sylib |
|
220 |
210 219
|
reximddv |
|
221 |
173 220
|
rexlimddv |
|
222 |
|
ge0nemnf |
|
223 |
44 61 222
|
syl2anc |
|
224 |
44 223
|
jca |
|
225 |
224
|
adantr |
|
226 |
|
xrnemnf |
|
227 |
225 226
|
sylib |
|
228 |
167 221 227
|
mpjaodan |
|
229 |
228
|
expr |
|
230 |
68 229
|
syl5 |
|
231 |
|
eleq2 |
|
232 |
|
eleq2 |
|
233 |
232
|
imbi2d |
|
234 |
233
|
rexralbidv |
|
235 |
231 234
|
imbi12d |
|
236 |
230 235
|
syl5ibrcom |
|
237 |
236
|
rexlimdva |
|
238 |
67 237
|
syl5bi |
|
239 |
238
|
ralrimiv |
|
240 |
|
xrstset |
|
241 |
1 240
|
resstset |
|
242 |
65 241
|
ax-mp |
|
243 |
8 242
|
topnval |
|
244 |
|
eqid |
|
245 |
27
|
a1i |
|
246 |
|
xrstps |
|
247 |
|
resstps |
|
248 |
246 65 247
|
mp2an |
|
249 |
1 248
|
eqeltri |
|
250 |
249
|
a1i |
|
251 |
8 243 244 245 250 2 3
|
eltsms |
|
252 |
63 239 251
|
mpbir2and |
|
253 |
|
letsr |
|
254 |
|
ordthaus |
|
255 |
253 254
|
mp1i |
|
256 |
|
resthaus |
|
257 |
255 65 256
|
sylancl |
|
258 |
8 245 250 2 3 243 257
|
haustsms2 |
|
259 |
252 258
|
mpd |
|